The solution of the equation $1 + a + {a^2} + {a^3} + ....... + {a^x}$ $ = (1 + a)(1 + {a^2})(1 + {a^4})$ is given by $x$ is equal to
$3$
$5$
$7$
None of these
The $G.M.$ of the numbers $3,\,{3^2},\,{3^3},....,\,{3^n}$ is
Which term of the following sequences:
$\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \ldots$ is $\frac{1}{19683} ?$
There are two such pairs of non-zero real valuesof $a$ and $b$ i.e. $(a_1,b_1)$ and $(a_2,b_2)$ for which $2a+b,a-b,a+3b$ are three consecutive terms of a $G.P.$, then the value of $2(a_1b_2 + a_2b_1) + 9a_1a_2$ is-
If $\frac{{a + bx}}{{a - bx}} = \frac{{b + cx}}{{b - cx}} = \frac{{c + dx}}{{c - dx}},\left( {x \ne 0} \right)$ then $a$, $b$, $c$, $d$ are in
If the sum of first 6 term is $9$ times to the sum of first $3$ terms of the same $G.P.$, then the common ratio of the series will be